Recognition of the dangers of ionizing radiation has become more focused over time. The recent focus on reducing dose became more urgent with the advent of cardiac Computed Tomography (CT). See for example, Raff, G.L., Radiation dose from coronary CT angiography: Five years of progress. Journal of Cardiovascular Computed Tomography (2010) 4, 365-374. These are inherently high dose procedures. Attempts to reduce dose include adaptive iterative reconstructions and modulating the tube potential during the scan. See for example, Sato, J., M. Akahane, S. Inano et al., Effect of radiation dose and adaptive statistical iterative reconstruction on image quality of pulmonary computed tomography. Jpn J Radiol (2012) 30:146-153; and Park, Y J Kim, J W Lee, et al. Automatic Tube Potential Selection with Tube Current Modulation (APSCM) in coronary CT angiography: Comparison of image quality and radiation dose with conventional body mass index-based protocol. Journal of Cardiovascular Computed Tomography (2012) 6, 184-190.
Suppose one is interested in reconstructing a region of interest (ROI) inside a patient. In our case the ROI is the cardiac region. Conventional (also known as global) reconstruction requires that the entire cross-section of the patient be irradiated. This means that during the scan one has to transmit x-rays through parts of the patient located far from the ROI. In the past 10-15 years, a group of algorithms called Local Tomography (LT) was developed. See, for example, Ramm A., and A. Katsevich, The Radon transform and local tomography, CRC Press, Boca Raton, Fla., 1996, and Katsevich, A., Improved cone beam local tomography, Inverse Problems 22 (2006), 627-643.
The main idea of LT is based on transmitting only those X-rays through the patient that intersect the Region of Interest (ROI) inside the patient. The X-rays that do not pass through the ROI are blocked from reaching the patient, which results in a reduction of the dose of a CT scan.
Conventional Computed Tomography (CT) reconstructs the distribution μ of the x-ray attenuation coefficient inside the object being scanned. Normally, μ is measured in Hounsfield units. Local Tomography (LT) computes not μ, but Bμ, where B is some operator that enhances singularities of μ (e.g., edges). Thus, the information about the actual values of μ inside the ROI is not recovered.
In two dimensions the main mathematical basis for LT is provided by the following two formulas (A) and (B):
                                          f            Λ                    =                                    1                              4                ⁢                π                                      ⁢                                          ∫                0                                  2                  ⁢                  π                                            ⁢                                                                    g                    ″                                    ⁡                                      (                                          α                      ,                                              α                        ·                        x                                                              )                                                  ⁢                                                                  ⁢                                  ⅆ                  α                                                                    ,                            (        A        )                                                      f            Λ                    =                                    F                              -                1                                      ⁡                          (                                                                  ξ                                                  ⁢                                                      f                    ~                                    ⁡                                      (                    ξ                    )                                                              )                                      ,                            (        B        )            where f is the Fourier transform of f; F−1 is the inverse Fourier transform; and g represents the CT data.
The fact that the first formula, A, contains only one integral demonstrates that LT reconstruction is local. The presence of the growing factor |ξ| in the second formula proves that LT enhances edges. The useful property of LT, which also follows from the second equation, is that it preserves all geometric features inside the ROI. In other words, the sharp features of μ (e.g., location of edges) coincide with sharp features of Bμ. See for example: Ramm A., and A. Katsevich, The Radon transform and local tomography, CRC Press, Boca Raton, Fla., 1996; and Faridani, A., K. Buglione, P. Huabsomboon, et al., Introduction to local tomography, Radon transforms and tomography. Contemp. Math., 278, Amer. Math. Soc, 2001, pp. 29-47. Thus, in some sense, LT is close to the gradient of the true image f.
In the cone beam setting (e.g., in helical scanning), the situation is more complicated. The reason is that B may add sharp features that are not present in μ. See for example, Katsevich, A., Cone beam local tomography, SIAM Journal on Applied Mathematics (1999), 2224-2246. This manifests itself as artifacts. However, it was shown by one of the subject inventors that by choosing an appropriate direction of filtering, one can significantly reduce the strength of the artifacts and potentially reduce dose. See for example, Katsevich, A., Improved cone beam local tomography, Inverse Problems 22 (2006), 627-643.
In classical cone beam LT the convolution kernel is very short, because it is equivalent to computing some kind of derivative on the detector. See for example, Louis A. K., and P. Maass, Contour reconstruction in 3-D X-ray CT, IEEE Transactions on Medical Imaging 12 (1993), 764-769 and Katsevich, A., Improved cone beam local tomography, Inverse Problems 22 (2006), 627-643.
A main disadvantage of LT is that LT images look different from conventional CT images, which may result in a loss of diagnostic information. Since LT emphasizes edges and does not reconstruct p in Hounsfield units it is sometimes hard to differentiate between tissue types and even see the presence of contrast.
Thus, the need exists for solutions to the above problems with the prior art.